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KatyaVom
@KatyaVom
July 2022
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ctg^4*2x-4ctg^2*2x+3=0 помогите, пожалуйста решить уравнение
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sangers1959
Verified answer
Ctg⁴(2x)-4*ctg²(2x)+3=0
ctg²(2x)=v
v²-4v+3=0 D=4
v=3 ctg²(2x)=3 ctg(2x)=+/-√3
ctg(2x)=√3 x₁=π/12+πn/2
ctg(2x)=-√3 x₂=-π/12+πn/2
v=1 ctg²(2x)=1 ctg(2x)=+/-√1 ctg(2x)=+/-1
x₃=π/8+πn/2 ctg(2x)=-1 x₄=-π/8+πn/2.
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Answers & Comments
Verified answer
Ctg⁴(2x)-4*ctg²(2x)+3=0ctg²(2x)=v
v²-4v+3=0 D=4
v=3 ctg²(2x)=3 ctg(2x)=+/-√3
ctg(2x)=√3 x₁=π/12+πn/2
ctg(2x)=-√3 x₂=-π/12+πn/2
v=1 ctg²(2x)=1 ctg(2x)=+/-√1 ctg(2x)=+/-1
x₃=π/8+πn/2 ctg(2x)=-1 x₄=-π/8+πn/2.